{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "# Ignore numpy dtype warnings. These warnings are caused by an interaction\n",
    "# between numpy and Cython and can be safely ignored.\n",
    "# Reference: https://stackoverflow.com/a/40846742\n",
    "warnings.filterwarnings(\"ignore\", message=\"numpy.dtype size changed\")\n",
    "warnings.filterwarnings(\"ignore\", message=\"numpy.ufunc size changed\")\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import nbinteract as nbi\n",
    "\n",
    "sns.set()\n",
    "sns.set_context('talk')\n",
    "np.set_printoptions(threshold=20, precision=2, suppress=True)\n",
    "pd.options.display.max_rows = 7\n",
    "pd.options.display.max_columns = 8\n",
    "pd.set_option('precision', 2)\n",
    "# This option stops scientific notation for pandas\n",
    "# pd.set_option('display.float_format', '{:.2f}'.format)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualization Principles Continued\n",
    "\n",
    "In this section, we discuss principles of visualization for transformation, context, and smoothing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principles of Transformation\n",
    "\n",
    "The principles of data transformation give us useful ways to alter data for visualization in order to more effectively reveal trends. We most commonly apply data transformations to reveal patterns in skewed data and non-linear relationships between variables.\n",
    "\n",
    "The plot below shows the distribution of ticket fares for each passenger aboard the Titanic. As you can see, the distribution is skewed right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4e/YsIiMjMWfOnFrz5xMTE7FlyxZs374dSUlJKC4uRlxcnME9xcXFePfdd1vND4pYXPkN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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1f73fc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ti = sns.load_dataset('titanic')\n",
    "sns.distplot(ti['fare'])\n",
    "plt.title('Fares for Titanic Passengers')\n",
    "plt.xlabel('Fare in USD')\n",
    "plt.ylabel('Density');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although this histogram shows the all the fares, it is difficult to see detailed patterns in the data since the fares are clumped on the left side of the histogram. To remedy this, we can take the natural log of the fares before plotting them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1azQqfHw8yMnJt7vd4l1Hz+Pu7kxBgb7Cw1l3RQTWcirr2fO2B/vOb8/ZQfL7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\niBBCCI9JEhFCCOGx/wBpIJtZr5unAgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a202c87b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(np.log(ti.loc[ti['fare'] > 0, 'fare']), bins=25)\n",
    "plt.title('log(Fares) for Titanic Passengers')\n",
    "plt.xlabel('log(Fare) in USD')\n",
    "plt.ylabel('Density');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the plot of the log data that the distribution of fares has a mode at roughly $ e^2 = \\$7.40 $ and a smaller mode at roughly $ e^{3.4} = \\$30.00 $. Why does plotting the natural log of the data help with skew? The logarithms of large numbers tend be close to the logarithms of small numbers:\n",
    "\n",
    "| value | log(value) |\n",
    "| ----- | ---------- |\n",
    "| 1     | 0.00       |\n",
    "| 10    | 2.30       |\n",
    "| 50    | 3.91       |\n",
    "| 100   | 4.60       |\n",
    "| 500   | 6.21       |\n",
    "| 1000  | 6.90       |\n",
    "\n",
    "This means that taking the logarithm of right-tailed data will bring large values close to small values. This helps see patterns where the majority of the data lie."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In fact, the logarithm is considered the Swiss army knife of data tranformation—it also helps us see the nature of non-linear relationships between variables in the data. In 1619, Kepler recorded down the following set of data to discover his Third Law of Planetary Motion:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>planet</th>\n",
       "      <th>mean_dist</th>\n",
       "      <th>period</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mercury</td>\n",
       "      <td>0.389</td>\n",
       "      <td>87.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Venus</td>\n",
       "      <td>0.724</td>\n",
       "      <td>224.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Earth</td>\n",
       "      <td>1.000</td>\n",
       "      <td>365.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Mars</td>\n",
       "      <td>1.524</td>\n",
       "      <td>686.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Jupiter</td>\n",
       "      <td>5.200</td>\n",
       "      <td>4332.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Saturn</td>\n",
       "      <td>9.510</td>\n",
       "      <td>10759.20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    planet  mean_dist    period\n",
       "0  Mercury      0.389     87.77\n",
       "1    Venus      0.724    224.70\n",
       "2    Earth      1.000    365.25\n",
       "3     Mars      1.524    686.95\n",
       "4  Jupiter      5.200   4332.62\n",
       "5   Saturn      9.510  10759.20"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "planets = pd.read_csv(\"data/planets.data\", delim_whitespace=True,\n",
    "                      comment=\"#\", usecols=[0, 1, 2])\n",
    "planets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we plot the mean distance to the sun against the period of the orbit, we can see a relationship that doesn't quite look linear:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x1a1f54aba8>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3LwoLCzF16lT06NEDQ4YMsdpYSTr0VQas2GIcVJWbHG+8EN7koNZQuskxtJ8/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\nHwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1f54ac88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='mean_dist', y='period', data=planets, ci=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, if we take the natural log of both mean distance and period, we obtain the following plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x1a1f693da0>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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QaHJODFSyupRzxVi5JQ31+oaJUF07tsPLk+JuOC+fyJkwUMmqfkm5ijU7s2Bq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1f6937b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='mean_dist', y='period',\n",
    "           data=np.log(planets.iloc[:, [1, 2]]),\n",
    "           ci=False);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see a near-perfect linear relationship between the logged values of mean distance and period. What does this mean? Since we believe there's a linear relationship between the logged values, we can derive:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\log(period) &= m \\log(dist) + b \\\\\n",
    "period &= e^{m \\log(dist) + b} & \\text{Taking the exponent of both sides} \\\\\n",
    "period &= e^b dist^m \\\\\n",
    "period &= C \\cdot dist^m\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "We replaced $ e^b $ with $ C $ in the last step to represent $ e^b $ as a constant. The algebraic manipulation above shows that when two variables have a polynomial relationship, the log of the two variables has a linear relationship. In fact, we can find the degree of the polynomial by examining the slope of the line. In this case, the slope is 1.5 which gives us Kepler's third law: $ period \\propto dist^{1.5} $.\n",
    "\n",
    "By a similar derivation we can also show that if the relationship between the $ \\log(y) $ and $ x $ is linear, the two variables have an exponential relationship: $ y = a^x $.\n",
    "\n",
    "Thus, we can use the logarithm to reveal patterns in right-tailed data and common non-linear relationships between variables.\n",
    "\n",
    "Other common data transformations include the Box-Cox transformation and polynomial transforms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principles of Context\n",
    "\n",
    "It is important to add as much relevant context as possible to any plot you plan to share more broadly. For example, the following plot shows its data clearly but provides little context to help understand what is being plotted.\n",
    "\n",
    "![viz_principles_img/viz_538_before.png](viz_principles_img/viz_538_before.png)\n",
    "\n",
    "To provide context, we add a title, caption, axes labels, units for the axes, and labels for the plotted lines.\n",
    "\n",
    "![viz_principles_img/viz_538_after.png](viz_principles_img/viz_538_after.png)\n",
    "\n",
    "([This blog post](https://www.dataquest.io/blog/making-538-plots/) explains how to make these modifications using `matplotlib`.)\n",
    "\n",
    "In general, we provide context for a plot through:\n",
    "\n",
    "- Plot title\n",
    "- Axes labels\n",
    "- Reference lines and markers for important values\n",
    "- Labels for interesting points and unusual observations\n",
    "- Captions that describe the data and its important features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principles of Smoothing\n",
    "\n",
    "Smoothing allows us to more clearly visualize data when we have many data points. We've actually already seen an instance of smoothing: histograms are a type of smoothing for rugplots. This rugplot shows each age of the passengers in the Titanic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a20c05b38>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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tRuGu58v3Xz6zYNCE7e3Kczv5vePUla/xas81ktE890jcbpc+OnFuyMwilZIycdh9YQN+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2081d080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ages = ti['age'].dropna()\n",
    "sns.rugplot(ages, height=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many marks that make it difficult to tell where the data lie. In addition, some of the points overlap, making it impossible to see how many points lie at 0. This issue is called *overplotting* and we generally avoid it whenever possible.\n",
    "\n",
    "To reveal the distribution of the data, we can replace groups of marks with a bar that is taller when more points are in the group. Smoothing refers to this process of replacing sets of points with appropriate markers; we choose not to show every single point in the dataset in order to reveal broader trends."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a23c384e0>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Nm6aLLrpIK1eulNfr1ZYtW1RbW6sZM2Zo8ODBysnJiVXtAIAwRRX2DQ0NKiws1IQJEyRJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a21fe4fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(ages, kde=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've also seen that `seaborn` will plot a smooth curve over a histogram by default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a23d89780>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wZMkSVq5cidVqdSmXl5fH5s2bycnJYffu3bS0tJCdne183GQy8etf/5rnnnvu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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a23cee978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(ages)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is another form of smoothing called *kernel density estimation* (KDE). Instead of grouping points together and plotting bars, KDE places a curve on each point and combines the individual curves to create a final estimation of the distribution. Consider the rugplot below that shows three points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IPQAYgNgDgAGIPQAYgNgDgAGIPQAYgNgDgAGIPQAYgNgDgAGIPQAYgNgDgAGIPQAYgNgD\ngAGIPQAYgNgDgAGIPQAYgNgDgAGIPQAYwFbsOzo6FAqFFAgEVF5erpMnT97w3t69e7V06VIVFBRo\n06ZN6uvrG9OxAIDRSRr7gYEBhcNhrV27Vq2traqsrNSGDRsUi8US7jU3N+vVV19VXV2d3nvvPV25\nckU7d+4ct+EAAPuSxr6lpUUej0cVFRXKyMhQKBRSbm6umpubE+41NTUpFArJ7/dr8uTJ2rhxoxob\nGzU0NDRu4wEA9qQnuxCJRJSXl5dw5vf71dnZqdLS0pGzrq4urVy5MuHO1atX9a9//UvTpk2zNcbj\nSbO7e0IZ3s1+Z7h5v5u3S+x3Wiq7k8a+r69PPp8v4czr9SoajSac9ff3y+v1jrw9/D79/f22x+Tk\nZNu+OxG5ef9bL5U7PeGmuH0/HzvOcvPrb1fSb+P4fL7rwh6NRpWVlZVw5vV6NTAwMPL2cOSzs7/8\nLyIATHRJYz9z5kxFIpGEs0gkojvvvDPhLC8vT11dXQl3Jk+erKlTp47RVADAaCWNfVFRkWKxmOrr\n6zU4OKjGxkb19PSouLg44d6DDz6o1157TZ2dnfrss8+0c+dOPfDAA/J4+FV+AHBammVZVrJLZ8+e\n1datW/Xhhx9qxowZ2rp1qwKBgKqqqhQMBhUOhyVJdXV12rt3r/7zn/+opKRE27Ztu+77/QCA/z5b\nsQcAuBvfYwEAAxB7ADAAsQcAAzgee7sPWZvoTp8+fd1vKLlBW1ubHn74YS1cuFArVqzQ/v37nZ6U\nkrffflurV69Wfn6+7r//fr377rtOT0pZT0+PioqKrnsEyUS3Z88efeMb31B+fv7In7a2Nqdn2fbx\nxx9r/fr1Kigo0D333KO6ujqnJ9n25ptvJrzu+fn5mjNnjrZs2fL572Q5KBqNWkuXLrV++9vfWrFY\nzHr99detJUuWWAMDA07OSkk8Hrdef/11a+HChVZhYaHTc1Jy+fJla9GiRVZTU5M1NDRktbe3W4sW\nLbKOHj3q9DRburq6rAULFlgnTpywLMuyjh49as2bN8/69NNPHV6Wmu9973vWnDlzrCNHjjg9JSVP\nPvmktWfPHqdnjEo8HrfWrFljbd++3YrFYta5c+esRYsWjXwsuc2xY8esJUuWWP/85z8/946jn9nb\nfcjaRFZbW6u6urqRXz91kwsXLqikpEQPPvigPB6P5s2bp7vvvlt//etfnZ5mi9/v19GjR1VQUKDe\n3l5dvHhR2dnZyszMdHqabfv27ZPP59Mdd9zh9JSUffDBB5o7d67TM0bl1KlTunjxojZt2qSMjAzN\nmjVL+/fvl9/vd3paynp7e/XTn/5UW7du1e233/659xyN/Rc9ZM0tHnroITU1NWn+/PlOT0nZ3Llz\n9eKLL468feXKFbW1tWnOnDkOrkpNdna2uru7FQwG9fTTT+uJJ57QLbfc4vQsW86fP69f//rX2rp1\nq9NTUtbf36/z58+rrq5OS5Ys0erVq9XY2Oj0LNvOnDmjWbNm6cUXX9SSJUtUWlqqU6dOKTc31+lp\nKduzZ49mz56tFStWfOG9pA9CG092H7I2kX1ZHgdx9epVhcNhzZs3T/fdd5/Tc1Jyxx136PTp02pr\na9MPfvADzZgxQ0VFRU7P+kLXrl3TU089pc2bNysnJ8fpOSnr6elRQUGBvv3tb2vnzp06ffq0wuGw\nbrvtNpWUlDg9L6krV67o+PHjWrx4sZqbm9Xe3q6qqipNnz5dwWDQ6Xm29fb2qqGhQbt3705619HP\n7O0+ZA3jq7u7W4888ohuvfVW/epXv3LdIy7S09OVkZGhoqIirVq1SocPH3Z6UlLV1dWaO3euK8J4\nI9OnT1dDQ4NKSkqUmZmpYDCo8vJyV7z2kpSZmalbb71V69evV2ZmpgoKClRaWuqa/cPeffddTZs2\nTYFAIOldR/9bbfchaxg/Z86c0bp161RcXKzq6uqEx1RPdO+9956+853vJJwNDg5q8uTJzgxKwdtv\nv61Dhw4pGAwqGAzqwoULevLJJ7Vr1y6np9ly5syZ67YODAy45uclfr9f/f39unbt2sjZ0NCQLJc9\nUKC5uVmrV6+2d/m/9/Pi6w0MDFjFxcVWXV3dyG/jLF682Ort7XVy1qi0tLS47rdxPvnkE2vx4sXW\nK6+84vSUUbl48aK1cOFC6w9/+IM1NDRk/eUvf7EKCgqsv//9705PS9m9997rqt/G6erqsubPn2+9\n88471tDQkHXs2DErEAhY7e3tTk+zpb+/31q6dKm1fft2a3Bw0Dpx4oQVCASsv/3tb05PS8myZcus\n999/39ZdR2NvWZb1wQcfWN/61resQCBglZeXu+7FHubG2NfU1FizZ8+2AoFAwp8dO3Y4Pc221tZW\na82aNVZ+fr61Zs0a2x/4E43bYm9ZlnX48GGrrKzMWrBggbVq1SrrnXfecXpSSs6fP2899thj1qJF\ni6x7773XamxsdHpSSq5du2bNmTPH9ic3PAgNAAzgrp/EAQBGhdgDgAGIPQAYgNgDgAGIPQAYgNgD\ngAGIPQAYgNgDgAGIPQAY4H8ArE8uMFdbyx0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2503ca58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = np.array([2, 3, 5])\n",
    "sns.rugplot(points, height=0.2)\n",
    "plt.xlim(0, 7);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To perform KDE, we place a Gaussian (normal) distribution on each point:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bYNremQM/SGPMZMPAKPewJSVezxMqD1upQI5yhDF82T5pYsnlq6uFv5OQ9jeT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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a273e98d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "def gaussians(points, scale=True, sd=0.5):\n",
    "    x_vals = [np.linspace(point - 2, point + 2, 100) for point in points]\n",
    "    y_vals = [norm.pdf(xs, loc=point, scale=sd) for xs, point in zip(x_vals, points)]\n",
    "    if scale:\n",
    "        y_vals = [ys / len(points) for ys in y_vals]\n",
    "    return zip(x_vals, y_vals)\n",
    "\n",
    "for xs, ys in gaussians(points, scale=False):\n",
    "    plt.plot(xs, ys, c=sns.color_palette()[0])\n",
    "\n",
    "sns.rugplot(points, height=0.2)\n",
    "plt.xlim(0, 7)\n",
    "plt.ylim(0, 1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The area under each Gaussian curve is equal to 1. Since we will sum multiple curves together, we scale each curve so that when added together the area under all the curves is equal to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wfyC7OTvg2aUTEObnxuU/455s/fXvC5X9CLPlN8zpq/XY/U0x9N2nax6Y6IMVs4Lg7iK1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\nRACo7AkhRACo7AkhRAD+P/ZL/vZtzBOyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a25b15a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for xs, ys in gaussians(points):\n",
    "    plt.plot(xs, ys, c=sns.color_palette()[0])\n",
    "\n",
    "sns.rugplot(points, height=0.2)\n",
    "plt.xlim(0, 7)\n",
    "plt.ylim(0, 1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we add the curves together to create a final smooth estimate for the distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7TvfIkMyd3xbh82O2ufZjwwbI7mL+kP7u+M29tovQuRdv4gDP39vFshfRuZJq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a25ea0f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.rugplot(points, height=0.2)\n",
    "sns.kdeplot(points, bw=0.5)\n",
    "plt.xlim(0, 7)\n",
    "plt.ylim(0, 1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By following this procedure, we can use KDE to smooth many points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HDpGYmOiklERbOS0dz62mUqn4+Y09ATh0vIKCM7L1p3B/fs2dUFBQQEJCgsOx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\nnreUewIYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a277aa208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show the original unsmoothed points\n",
    "sns.rugplot(ages, height=0.1)\n",
    "\n",
    "# Show the smooth estimation of the distribution\n",
    "sns.kdeplot(ages);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kernel Density Estimation Details"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the previous examples of KDE, we placed a miniature Gaussian curve on each point and added the Gaussians together. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wfyC7OTvg2aUTEObnxuU/455s/fXvC5X9CLPlN8zpq/XY/U0x9N2nax6Y6IMVs4Lg7iK1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\nRACo7AkhRACo7AkhRAD+P/ZL/vZtzBOyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a25b15a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for xs, ys in gaussians(points):\n",
    "    plt.plot(xs, ys, c=sns.color_palette()[0])\n",
    "\n",
    "sns.rugplot(points, height=0.2)\n",
    "plt.xlim(0, 7)\n",
    "plt.ylim(0, 1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are free to adjust the width of the Gaussians. For example, we can make each Gaussian narrower. This is called decreasing the *bandwidth* of the kernel estimation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vj7uYsVqbQsbVLeT6v3WFZXZaDKJveehlpPpXLorHu6X1sFgdOHnpGu5ePjt4xd7CYrPj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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a272f1390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for xs, ys in gaussians(points, sd=0.3):\n",
    "    plt.plot(xs, ys, c=sns.color_palette()[0])\n",
    "\n",
    "sns.rugplot(points, height=0.2)\n",
    "plt.xlim(0, 7)\n",
    "plt.ylim(0, 1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we add these narrower Gaussians together, we create a more detailed final estimation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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oLJN97K+n3GkDAAxkeBOQ4YnsVhJd/9mUSojHPTpZCWUyZsca2LkPBCPwBWjj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\nsycIgtABZPYEQRA6gMyeIAhCB/x/jIiizWz6gz0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a273c0f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.rugplot(points, height=0.2)\n",
    "sns.kdeplot(points, bw=0.2)\n",
    "plt.xlim(0, 7)\n",
    "plt.ylim(0, 1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iT7Em3yS9rMiMaeMLe118ra+Rev5m4UmF3dg48DeAaPGXwqJ+ANAItg95/oSS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\n3R5jyIl1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a286b7c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the KDE for Titanic passenger ages using a lower bandwidth\n",
    "sns.rugplot(ages, height=0.1)\n",
    "sns.kdeplot(ages, bw=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just like adjusting bins for a histogram, we typically adjust the bandwidth until we believe the final plot shows the distribution without distracting the viewer with too much detail.\n",
    "\n",
    "Although we have placed a Gaussian at each point so far, we can easily select other functions to estimate each point. This is called changing the *kernel* of the kernel density estimation. Previously, we've used a Gaussian kernel. Now, we'll use a triangular kernel which places a pair of stepwise sloped lines at each point:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a26eb3908>"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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C94Y6CSNj0IBS4Pmb6EqB13uhTfmZE+kC96dauY2q56rvuhNDThHm0LCxipoC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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a271e2390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.rugplot(points, height=0.2)\n",
    "sns.kdeplot(points, kernel='tri', bw=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Q92EzMWg0GuTm5mLlypU4ffo01qxZgw0bNkCr1VqVKywsxL59+5Cfn48TJ06gs7MTeXl5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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2859c908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the KDE for Titanic passenger ages using a triangular kernel\n",
    "sns.rugplot(ages, height=0.1)\n",
    "sns.kdeplot(ages, kernel='tri');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Usually we'll use a Gaussian kernel unless we have a specific reason to use a different kernel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Smoothing a Scatter Plot\n",
    "\n",
    "We can also smooth two-dimensional plots when we encounter the problem of overplotting.\n",
    "\n",
    "The following example comes from a dataset released by the Cherry Blossom Run, an annual 10-mile run in Washington D.C. Each runner can report their age and their race time; we've plotted all the reported data points in the scatter plot below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>place</th>\n",
       "      <th>age</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1999</td>\n",
       "      <td>1</td>\n",
       "      <td>28.0</td>\n",
       "      <td>2819.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1999</td>\n",
       "      <td>2</td>\n",
       "      <td>24.0</td>\n",
       "      <td>2821.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1999</td>\n",
       "      <td>3</td>\n",
       "      <td>27.0</td>\n",
       "      <td>2823.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70066</th>\n",
       "      <td>2012</td>\n",
       "      <td>7190</td>\n",
       "      <td>56.0</td>\n",
       "      <td>8840.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70067</th>\n",
       "      <td>2012</td>\n",
       "      <td>7191</td>\n",
       "      <td>35.0</td>\n",
       "      <td>8850.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70069</th>\n",
       "      <td>2012</td>\n",
       "      <td>7193</td>\n",
       "      <td>48.0</td>\n",
       "      <td>9059.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>70045 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       year  place   age    time\n",
       "0      1999      1  28.0  2819.0\n",
       "1      1999      2  24.0  2821.0\n",
       "2      1999      3  27.0  2823.0\n",
       "...     ...    ...   ...     ...\n",
       "70066  2012   7190  56.0  8840.0\n",
       "70067  2012   7191  35.0  8850.0\n",
       "70069  2012   7193  48.0  9059.0\n",
       "\n",
       "[70045 rows x 4 columns]"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "runners = pd.read_csv('data/cherryBlossomMen.csv').dropna()\n",
    "runners"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WBjUej2P8+PHYvHmz89gdd9yBu+66C3v37kVTUxMmTJgAAGhsbERdXR0qKytR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\niSPtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a275d63c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='age', y='time', data=runners, fit_reg=False);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So many points lie on top of each other that it's difficult to see any trend at all!\n",
    "\n",
    "We can smooth the scatter plot using kernel density estimation in two dimensions. When KDE is applied to a two-dimensional plot, we place a three-dimensional Gaussian at each point. In three dimensions, the Gaussian looks like a mountain pointing out of the page."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a211189e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot three points\n",
    "two_d_points = pd.DataFrame({'x': [1, 3, 4], 'y': [4, 3, 1]})\n",
    "sns.lmplot(x='x', y='y', data=two_d_points, fit_reg=False)\n",
    "plt.xlim(-2, 7)\n",
    "plt.ylim(-2, 7);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vzXsZn9+HJEn8+PwfcfHZFyJJEnV1tfzmN3fS3NyETqfjj398lIEDB5+QOB2i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\nGzZw3nnn9focsiw2IzmWQzESsTo6Eaf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GXtt97Hns6vGaAoSJO7aX4Q8HIo99oQDWr1eO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\nRJFwEEIIEUXCQQghRJT/D8bZuq3vhY60AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a258b4ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Place a Gaussian at each point and use a contour plot to show each one\n",
    "sns.kdeplot(two_d_points['x'], two_d_points['y'], bw=0.4)\n",
    "plt.xlim(-2, 7)\n",
    "plt.ylim(-2, 7);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just like we've previously seen, we scale each Gaussian and add them together to obtain a final contour plot for the scatter plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Zx+i3T+BdgXeS/NLWk38JW8JSyCRSUjUGsrTJFOjTyIxKWnKF4Q36aZnr5YSx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\nhBDCioSDEEIIK/8HJ4TV9tCetjoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a29731710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(two_d_points['x'], two_d_points['y'])\n",
    "plt.xlim(-2, 7)\n",
    "plt.ylim(-2, 7);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting plot shows the downward sloping trend of the three points. Similarly, we can apply a KDE to smooth out the scatter plot of runner ages and times:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jZ0pKijtZUfsjGI6AwF9ITtZWyjQxMW1ccNzAmYva7AMuDs707NHUTGqVdfzf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\nU0VdY12fYpVKpHi7eRHsG0yIX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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a25850358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(runners['age'], runners['time'])\n",
    "plt.xlim(-10, 70)\n",
    "plt.ylim(3000, 8000);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that most of our runners were between 25 and 50 years old, and that most runners took between 4000 and 7000 seconds (roughly between 1 and 2 hours) to finish the race.\n",
    "\n",
    "We can see more clearly that there is a suspicious group of runners that are between zero and ten years old. We might want to double check that our data for those ages was recorded properly.\n",
    "\n",
    "We can also see a slight upward trend in the time taken to finish the race as runner age increases."
   ]
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
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    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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   "name": "python",
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  "toc": {
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   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
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}
